Dimensional Transmutation and Dimensional Regularization in Quantum Mechanics I. General Theory
Dimensional Transmutation and Dimensional Regularization in Quantum Mechanics I. General Theory
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DOI：
10.1006/aphy.2000.6092
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发表时间：
2000-03
影响因子：
3
通讯作者：
H. Camblong;L. Epele;H. Fanchiotti;C. Canal
中科院分区：
文献类型：
--
作者：
H. Camblong;L. Epele;H. Fanchiotti;C. Canal
本文是在维数正则化框架下讨论非相对论量子力学中维数嬗变现象的系列论文中的第一篇。标度不变的潜力确定和他们的一般性质的推导。这些系统在强耦合制度的维度重整化的策略，并显示出的能量尺度的出现，无论是对于束缚态和散射部门。最后，明确地说明了二维δ函数势的尺寸嬗变。
Abstract This is the first in a series of papers addressing the phenomenon of dimensional transmutation in nonrelativistic quantum mechanics within the framework of dimensional regularization. Scale-invariant potentials are identified and their general properties are derived. A strategy for dimensional renormalization of these systems in the strong-coupling regime is presented, and the emergence of an energy scale is shown, both for the bound-state and scattering sectors. Finally, dimensional transmutation is explicitly illustrated for the two-dimensional delta-function potential.